Bring pineapple, 1/2 cup reserved pineapple juice, and 1/2 cup sugar to a boil in a 2- to 3-quart heavy saucepan, stirring until sugar is dissolved.

Reduce heat and simmer, stirring occasionally, until pineapple is softened, about 5 minutes.

Stir together cornstarch and remaining tablespoon pineapple juice in a small bowl until cornstarch is dissolved, then add to pineapple mixture and simmer, stirring frequently, until thickened, about 1 minute.

Bring milk just to a boil in a 1 1/2- to 2-quart heavy saucepan.

Whisk together yolks, remaining 1/4 cup plus 2 tablespoons sugar, and a large pinch of salt in a bowl, then add hot milk in a stream, whisking.

Pour custard back into saucepan and cook over moderately low heat, stirring with a wooden spoon, until custard registers 170 to 175°F on thermometer, 2 to 3 minutes.

Immediately pour custard through a very fine-mesh sieve into a bowl, then stir in pineapple mixture and vanilla and cool to room temperature, stirring occasionally.

Stir the cream, then chill custard, covered, until very cold, about 4 hours.

Freeze custard in ice cream maker.

Transfer ice cream to an airtight container and put in freezer to harden, at least 12 hours.